Automatically Generating Formulas Based on Parameters of a Model

1. A computer-based method, comprising: receiving, by a computer, model specification data specifying: a dimensional operation associated with a plurality of generation methods; a dimension that corresponds to a quantity over which interval arithmetic is defined, the dimension including at least one segment; an analysis variable having an input formula for determining values of the analysis variable along the dimension; and an operational type associated with the analysis variable and the dimensional operation, the operational type specifying a generation method from the plurality of generation methods; identifying, by the computer, the generation method based on the analysis variable, the dimensional operation and the operational type; generating a first set of arguments for the input formula for a first set of one or more segments of the dimension, wherein generating the first set of arguments for the input formula for the first set of one or more segments includes generating the first set of arguments for the input formula for multiple non-overlapping ranges of the quantity; automatically generating, by the computer, an output formula from the input formula using the generation method, wherein automatically generating the output formula comprises processing the first set of arguments according to the generation method to generate a second set of arguments for the input formula for a second set of one or more segments of the dimension different from the first set of one or more segments of the dimension; and storing, by the computer, the automatically generated output formula or presenting, by the computer, a representation based on the automatically generated output formula using a user interface, wherein receiving the model specification data includes receiving model specification data specifying that the dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in second set of one or more segments.

2. The method of claim 1 , further comprising generating multiple output formulas from the input formula, each output formula corresponding to a different segment of the dimension.

3. The method of claim 2 , wherein automatically generating the output formula comprises generating the output formula from the input formula for a combination of multiple segments of the dimension.

4. The method of claim 1 , further comprising generating a segment output formula from the input formula for a segment of the dimension.

5. The method of claim 4 , wherein automatically generating the segment output formula comprises generating multiple output formulas from the input formula for different subsegments of the segment of the dimension.

6. The method of claim 1 , wherein the automatically generated output formula comprises a formula in a cell of a spreadsheet generated based on the second set of arguments for the second set of one or more segments of the dimension.

7. The method of claim 1 , wherein receiving the model specification data includes receiving model specification data specifying that the dimension corresponds to time.

8. The method of claim 1 , wherein generating the first set of arguments for the input formula for the first set of one or more segments includes generating the first set of arguments for the input formula for at least one range of the quantity and wherein receiving the model specification data includes receiving model specification data specifying that the dimension be associated with a dimensional operation that splits at least one range into multiple non-overlapping ranges of the quantity in the second set of one or more segments.

9. The method of claim 1 , wherein automatically generating the output formula comprises determining one of multiple valid ways to apply the generation method to generate the second set of arguments based at least in part on feedback from a user.

10. The method of claim 1 , wherein receiving the model specification data includes receiving model specification data specifying that the at least one segment include a plurality of segments capable of being interrelated in a hierarchy wherein each parent in the hierarchy corresponds to a segment that is a combination of segments corresponding to children of the parent.

11. The method of claim 10 , wherein receiving the model specification data includes receiving model specification data specifying that the dimension be associated with a dimensional operation that specifies generation of arguments for segments corresponding to a first level in the hierarchy based on one or more input formulas for segments corresponding to a second level in the hierarchy different from the first level.

12. The method of claim 1 , wherein receiving the model specification data includes receiving model specification data specifying that the input formula of the analysis variable includes a first set of one or more analysis variables that each depend on the dimension.

13. The method of claim 12 , wherein receiving the model specification data includes receiving model specification data specifying that the dimensional operation associated with the dimension specifies generation of a second set of one or more analysis variables based on the first set of one or more analysis variables.

14. The method of claim 13 , wherein automatically generating the output formula comprises applying the input formula to the second set of one or more analysis variables.

15. A non-transitory computer-readable medium having stored therein instructions for causing a computer to: receive model specification data specifying: a dimensional operation associated with a plurality of generation methods; a dimension that corresponds to a quantity over which interval arithmetic is defined, the dimension including at least one segment; an analysis variable having an input formula for determining values of the analysis variable along the dimension; and an operational type associated with the analysis variable and the dimensional operation, the operational type specifying a generation method from the plurality of generation methods; identify, the generation method based on the analysis variable, the dimensional operation and the operational type; generate a first set of arguments for the input formula for a first set of one or more segments of the dimension, the first set of one or more segments including multiple non-overlapping ranges of the quantity; automatically generate an output formula from the input formula using the generation method by processing the first set of arguments according to the generation method to generate a second set of arguments for the input formula for a second set of one or more segments of the dimension different from the first set of one or more segments of the dimension; and store the automatically generated output formula or present a representation based on the automatically generated output formula using a user interface, wherein the instructions for causing the computer to receive the model specification data include instructions to receive model specification data specifying that the dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in the second set of one or more segments.

16. A computer-based method, comprising: receiving, by a computer, model specification data specifying: at least one dimension that corresponds to a quantity over which interval arithmetic is defined, the at least one dimension being associated with a hierarchy; an analysis variable that has an operational type and that depends on the at least one dimension; and a dimensional operation that in combination with the analysis variable and the operational type specifies a first input formula that determines values for the analysis variable where the analysis variable is associated with one or more levels of the hierarchy and a second input formula different from the first input formula that determines a combination of multiple values from a given level of the hierarchy for the analysis variable where the analysis variable is associated with a different level of the hierarchy; generating a first set of arguments for the first input formula for a first set of one or more segments of the at least one dimension, wherein generating the first set of arguments for the first input formula for the first set of one or more segments includes generating the first set of arguments for the first input formula for multiple non-overlapping ranges of the quantity; automatically generating, by the computer, an output formula from the analysis variable, wherein automatically generating the output formula comprises processing the first set of arguments according to a generation method to generate a second set of arguments for the first input formula for a second set of one or more segments of the at least one dimension different from the first set of one or more segments of the at least one dimension; and storing, by the computer, the automatically generated output formula or presenting, by the computer, a representation based on the automatically generated output formula using a user interface, wherein receiving the model specification data includes receiving model specification data specifying that the at least one dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in the second set of one or more segments.

17. The method of claim 16 , wherein receiving the model specification data includes receiving model specification data specifying that the hierarchy associated with the at least one dimension corresponds to a graph of nodes having a tree structure where each node represents a segment of the dimension, and the segment represented by a given parent node is based on a combination of segments represented by child nodes of the given parent node.

18. The method of claim 17 , wherein receiving the model specification data includes receiving model specification data specifying that the first input formula is associated with a corresponding node.

19. The method of claim 18 , wherein receiving the model specification data includes receiving model specification data specifying that the first input formula determines a value of the corresponding node if the corresponding node is a leaf node or of a subordinate node if the corresponding node is not a leaf node.

20. The method of claim 17 , wherein receiving the model specification data includes receiving model specification data specifying that the second input formula is associated with a corresponding node.

21. The method of claim 20 , wherein receiving the model specification data includes receiving model specification data specifying that the analysis variable specifies one of multiple default operators for performing a dimensional operation that includes combining segments represented by child nodes of a parent node.

22. The method of claim 21 , wherein receiving the model specification data includes receiving model specification data specifying that the second input formula determines a combination of values of child nodes of the corresponding node in place of the specified default operator.

23. The method of claim 20 , wherein receiving the model specification data includes receiving model specification data specifying that the second input formula determines a value for the corresponding node if the corresponding node is a leaf node and no other formula determines a value for the corresponding node.

24. The method of claim 20 , wherein receiving the model specification data includes receiving model specification data specifying that the second input formula determines a value for the corresponding node based on a combination of values of child nodes of the corresponding node that are added in a dimensional operation that includes splitting the segment represented by the corresponding node into multiple segments.

25. The method of claim 17 , wherein receiving the model specification data includes receiving model specification data specifying that segments have a predetermined ordering.

26. The method of claim 17 , wherein receiving the model specification data includes receiving model specification data specifying that the first input formula is associated with a first level of the hierarchy and the second input formula is associated with a second level of the hierarchy different from the first level.

27. The method of claim 26 , wherein receiving the model specification data includes receiving model specification data specifying that the first input formula determines a value for at least one leaf node.

28. The method of claim 27 , wherein receiving the model specification data includes receiving model specification data specifying that the second input formula determines a combination of values of child nodes of a parent node at the second level.

29. The method of claim 17 , wherein receiving the model specification data includes receiving model specification data specifying that the first input formula and second input formula are associated with the same non-leaf node.

30. The method of claim 29 , further comprising determining values for child nodes of the non-leaf node so that the combination determined by the second input formula is consistent with a value determined by the first input formula.

31. The method of claim 29 , further comprising determining a value for the non-leaf node based on the combination determined by the second input formula even if a value determined by the first input formula is different from the combination determined by the second input formula.

32. A non-transitory computer-readable medium having stored therein instructions for causing a computer to: receive model specification data specifying: at least one dimension that corresponds to a quantity over which interval arithmetic is defined, the at least one dimension being associated with a hierarchy; an analysis variable that has an operational type that depends on the at least one dimension; and a dimensional operation that in combination with the analysis variable and the operational type specifies a first input formula that determines values for one or more levels of the hierarchy and a second input formula different from the first input formula that determines a combination of multiple values from a given level of the hierarchy for a different level of the hierarchy; generate a first set of arguments for the first input formula for a first set of one or more segments of the at least one dimension, the first set of one or more segments including multiple non-overlapping ranges of the quantity; automatically generate an output formula from the analysis variable by processing the first set of arguments according to a generation method to generate a second set of arguments for the first input formula for a second set of one or more segments of the at least one dimension different from the first set of one or more segments of the at least one dimension; and store the automatically generated output formula or present a representation based on the automatically generated output formula using a user interface, wherein the instructions for causing the computer to receive the model specification data include instructions to receive model specification data specifying that the at least one dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in the second set of one or more segments.

33. The method of claim 1 , wherein receiving the model specification data includes receiving model specification data specifying that the analysis variable has an input formula written in terms of analysis variables and generating the output formula includes generating an output formula written in terms of a table of cells.

34. A computer system comprising: a memory; and at least one processor coupled to the memory and configured to: receive model specification data specifying: a dimensional operation associated with a plurality of generation methods; a dimension that corresponds to a quantity over which interval arithmetic is defined, the dimension including at least one segment; an analysis variable having an input formula for determining values of the analysis variable along the dimension; and an operational type associated with the analysis variable and the dimensional operation, the operational type specifying a generation method of the plurality of generation methods; identify the generation method based on the analysis variable, the dimensional operation, and the operational type; generate a first set of arguments for the input formula for a first set of one or more segments of the dimension, the first set of one or more segments including multiple non-overlapping ranges of the quantity; automatically generate an output formula from the input formula using the generation method by processing the first set of arguments according to the generation method to generate a second set of arguments for the input formula for a second set of one or more segments of the dimension different from the first set of one or more segments of the dimension; and store the automatically generated output formula or present a representation based on the automatically generated output formula using a user interface, wherein the at least one processor is configured to receive the model specification data by receiving model specification data specifying that the dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in the second set of one or more segments.

35. A computer system comprising: a memory; and at least one processor coupled to the memory and configured to: receive model specification data specifying: at least one dimension that corresponds to a quantity over which interval arithmetic is defined, the at least one dimension associated with a hierarchy; an analysis variable that has an operational type and that depends on the at least one dimension; and a dimensional operation that in combination with the analysis variable and the operational type specifies a first input formula that determines values for the analysis variable where the analysis variable is associated with one or more levels of the hierarchy and a second input formula different from the first input formula that determines a combination of multiple values from a given level of the hierarchy for the analysis variable where the analysis variable is associated with a different level of the hierarchy; generate a first set of arguments for the first input formula for a first set of one or more segments of the at least one dimension, the first set of one or more segments including multiple non-overlapping ranges of the quantity; automatically generate an output formula from the analysis variable by processing the first set of arguments according to a generation method to generate a second set of arguments for the first input formula for a second set of one or more segments of the at least one dimension different from the first set of one or more segments of the at least one dimension; and store the automatically generated output formula or present a representation based on the automatically generated output formula using a user interface, wherein the at least one processor is configured to receive the model specification data by receiving model specification data specifying that the at least one dimension be associated with a dimensional operation that combines one or more of the ranges into at least one combined range of the quantity in the second set of one or more segments.

36. The method of claim 1 , wherein generating the output formula written in terms of a table of cells includes generating an output formula written in terms of cells a spreadsheet.